OpenRaiser/Intern-Atlas huggingface dataset:
Representation, Approximation and Learning of Submodular Functions Using Low-rank Decision Trees
Venue: arXiv cs.LG 2013
Year: 2013

We study the complexity of approximate representation and learning of submodular functions over the uniform distribution on the Boolean hypercube $\{0,1\}^n$. Our main result is the following structural theorem: any submodular function is $ε$-close in $\ell_2$ to a real-valued decision tree (DT) of depth $O(1/ε^2)$. This immediately implies that any submodular function is $ε$-close to a function of at most $2^{O(1/ε^2)}$ variables and has a spectral $\ell_1$ norm of $2^{O(1/ε^2)}$. It also implies the closest previous result that states that submodular functions can be approximated by polynomials of degree $O(1/ε^2)$ (Cheraghchi et al., 2012). Our result is proved by constructing an approximation of a submodular function by a DT of rank $4/ε^2$ and a proof that any rank-$r$ DT can be $ε$-approximated by a DT of depth $\frac{5}{2}(r+\log(1/ε))$. We show that these structural results can be exploited to give an attribute-efficient PAC learning algorithm for submodular functions running in time $\tilde{O}(n^2) \cdot 2^{O(1/ε^{4})}$. The best previous algorithm for the problem requires $n^{O(1/ε^{2})}$ time and examples (Cheraghchi et al., 2012) but works also in the agnostic setting. In addition, we give improved learning algorithms for a number of related settings. We also prove that our PAC and agnostic learning algorithms are essentially optimal via two lower bounds: (1) an information-theoretic lower bound of $2^{Ω(1/ε^{2/3})}$ on the complexity of learning monotone submodular functions in any reasonable model; (2) computational lower bound of $n^{Ω(1/ε^{2/3})}$ based on a reduction to learning of sparse parities with noise, widely-believed to be intractable. These are the first lower bounds for learning of submodular functions over the uniform distribution.
On the State Complexity of the Reverse of R- and J-trivial Regular Languages
Venue: arXiv cs.FL 2013
Year: 2013

The tight upper bound on the state complexity of the reverse of R-trivial and J-trivial regular languages of the state complexity n is 2^{n-1}. The witness is ternary for R-trivial regular languages and (n-1)-ary for J-trivial regular languages. In this paper, we prove that the bound can be met neither by a binary R-trivial regular language nor by a J-trivial regular language over an (n-2)-element alphabet. We provide a characterization of tight bounds for R-trivial regular languages depending on the state complexity of the language and the size of its alphabet. We show the tight bound for J-trivial regular languages over an (n-2)-element alphabet and a few tight bounds for binary J-trivial regular languages. The case of J-trivial regular languages over an (n-k)-element alphabet, for 2 <= k <= n-3, is open.
Network Access Control Technology - Proposition to contain new security challenges
Venue: arXiv cs.CR 2013
Year: 2013

Traditional products working independently are no longer sufficient, since threats are continually gaining in complexity, diversity and performance; In order to proactively block such threats we need more integrated information security solution. To achieve this objective, we will analyze a real-world security platform, and focus on some key components Like, NAC, Firewall, and IPS/IDS then study their interaction in the perspective to propose a new security posture that coordinate and share security information between different network security components, using a central policy server that will be the NAC server or the PDP (the Policy Decision Point), playing an orchestration role as a central point of control. Finally we will conclude with potential research paths that will impact NAC technology evolution.
Bose-Einstein Condensation in Satisfiability Problems
Venue: arXiv cs.DS 2013
Year: 2013

This paper is concerned with the complex behavior arising in satisfiability problems. We present a new statistical physics-based characterization of the satisfiability problem. Specifically, we design an algorithm that is able to produce graphs starting from a k-SAT instance, in order to analyze them and show whether a Bose-Einstein condensation occurs. We observe that, analogously to complex networks, the networks of k-SAT instances follow Bose statistics and can undergo Bose-Einstein condensation. In particular, k-SAT instances move from a fit-get-rich network to a winner-takes-all network as the ratio of clauses to variables decreases, and the phase transition of k-SAT approximates the critical temperature for the Bose-Einstein condensation. Finally, we employ the fitness-based classification to enhance SAT solvers (e.g., ChainSAT) and obtain the consistently highest performing SAT solver for CNF formulas, and therefore a new class of efficient hardware and software verification tools.
Improved Analytical Delay Models for RC-Coupled Interconnects
Venue: arXiv cs.AR 2013
Year: 2013

As the process technologies scale into deep submicron region, crosstalk delay is becoming increasingly severe, especially for global on-chip buses. To cope with this problem, accurate delay models of coupled interconnects are needed. In particular, delay models based on analytical approaches are desirable, because they not only are largely transparent to technology, but also explicitly establish the connections between delays of coupled interconnects and transition patterns, thereby enabling crosstalk alleviating techniques such as crosstalk avoidance codes (CACs). Unfortunately, existing analytical delay models, such as the widely cited model in [1], have limited accuracy and do not account for loading capacitance. In this paper, we propose analytical delay models for coupled interconnects that address these disadvantages. By accounting for more wires and eschewing the Elmore delay, our delay models achieve better accuracy than the model in [1].
Predicting Network Attacks Using Ontology-Driven Inference
Venue: arXiv cs.AI 2013
Year: 2013

Graph knowledge models and ontologies are very powerful modeling and re asoning tools. We propose an effective approach to model network attacks and attack prediction which plays important roles in security management. The goals of this study are: First we model network attacks, their prerequisites and consequences using knowledge representation methods in order to provide description logic reasoning and inference over attack domain concepts. And secondly, we propose an ontology-based system which predicts potential attacks using inference and observing information which provided by sensory inputs. We generate our ontology and evaluate corresponding methods using CAPEC, CWE, and CVE hierarchical datasets. Results from experiments show significant capability improvements comparing to traditional hierarchical and relational models. Proposed method also reduces false alarms and improves intrusion detection effectiveness.
Toward Evolution Strategies Application in Automatic Polyphonic Music Transcription using Electronic Synthesis
Venue: arXiv cs.SD 2013
Year: 2013

We present in this paper a new approach for polyphonic music transcription using evolution strategies (ES). Automatic music transcription is a complex process that still remains an open challenge. Using an audio signal to be transcribed as target for our ES, information needed to generate a MIDI file can be extracted from this latter one. Many techniques presented in the literature at present exist and a few of them have applied evolutionary algorithms to address this problem in the context of considering it as a search space problem. However, ES have never been applied until now. The experiments showed that by using these machines learning tools, some shortcomings presented by other evolutionary algorithms based approaches for transcription can be solved. They include the computation cost and the time for convergence. As evolution strategies use self-adapting parameters, we show in this paper that by correctly tuning the value of its strategy parameter that controls the standard deviation, a fast convergence can be triggered toward the optima, which from the results performs the transcription of the music with good accuracy and in a short time. In the same context, the computation task is tackled using parallelization techniques thus reducing the computation time and the transcription time in the overall.
On optimal language compression for sets in PSPACE/poly
Venue: arXiv cs.CC 2013
Year: 2013

We show that if DTIME[2^O(n)] is not included in DSPACE[2^o(n)], then, for every set B in PSPACE/poly, all strings x in B of length n can be represented by a string compressed(x) of length at most log(|B^{=n}|)+O(log n), such that a polynomial-time algorithm, given compressed(x), can distinguish x from all the other strings in B^{=n}. Modulo the O(log n) additive term, this achieves the information-theoretic optimum for string compression. We also observe that optimal compression is not possible for sets more complex than PSPACE/poly because for any time-constructible superpolynomial function t, there is a set A computable in space t(n) such that at least one string x of length n requires compressed(x) to be of length 2 log(|A^=n|).
A Novel Frank-Wolfe Algorithm. Analysis and Applications to Large-Scale SVM Training
Venue: arXiv cs.CV 2013
Year: 2013

Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as {the Frank-Wolfe (FW) method}. In particular, this procedure has been successfully applied to train large-scale instances of non-linear Support Vector Machines (SVMs). Specializing FW to SVM training has allowed to obtain efficient algorithms but also important theoretical results, including convergence analysis of training algorithms and new characterizations of model sparsity. In this paper, we present and analyze a novel variant of the FW method based on a new way to perform away steps, a classic strategy used to accelerate the convergence of the basic FW procedure. Our formulation and analysis is focused on a general concave maximization problem on the simplex. However, the specialization of our algorithm to quadratic forms is strongly related to some classic methods in computational geometry, namely the Gilbert and MDM algorithms. On the theoretical side, we demonstrate that the method matches the guarantees in terms of convergence rate and number of iterations obtained by using classic away steps. In particular, the method enjoys a linear rate of convergence, a result that has been recently proved for MDM on quadratic forms. On the practical side, we provide experiments on several classification datasets, and evaluate the results using statistical tests. Experiments show that our method is faster than the FW method with classic away steps, and works well even in the cases in which classic away steps slow down the algorithm. Furthermore, these improvements are obtained without sacrificing the predictive accuracy of the obtained SVM model.
Spatial Resources Optimization in Distributed MIMO Networks with Limited Data Sharing
Venue: arXiv cs.IT 2013
Year: 2013

Wireless access through a large distributed network of low-complexity infrastructure nodes empowered with cooperation and coordination capabilities, is an emerging radio architecture, candidate to deal with the mobile data capacity crunch. In the 3GPP evolutionary path, this is known as the Cloud-RAN paradigm for future radio. In such a complex network, distributed MIMO resources optimization is of paramount importance, in order to achieve capacity scaling. In this paper, we investigate efficient strategies towards optimizing the pairing of access nodes with users as well as linear precoding designs for providing fair QoS experience across the whole network, when data sharing is limited due to complexity and overhead constraints. We propose a method for obtaining the exact optimal spatial resources allocation solution which can be applied in networks of limited scale, as well as an approximation algorithm with bounded polynomial complexity which can be used in larger networks. The particular algorithm outperforms existing user-oriented clustering techniques and achieves quite high quality-of-service levels with reasonable complexity.
On Heuristics for Finding Loop Cutsets in Multiply-Connected Belief Networks
Venue: arXiv cs.AI 2013
Year: 2013

We introduce a new heuristic algorithm for the problem of finding minimum size loop cutsets in multiply connected belief networks. We compare this algorithm to that proposed in [Suemmondt and Cooper, 1988]. We provide lower bounds on the performance of these algorithms with respect to one another and with respect to optimal. We demonstrate that no heuristic algorithm for this problem cam be guaranteed to produce loop cutsets within a constant difference from optimal. We discuss experimental results based on randomly generated networks, and discuss future work and open questions.
Updating with Belief Functions, Ordinal Conditioning Functions and Possibility Measures
Venue: arXiv cs.AI 2013
Year: 2013

This paper discusses how a measure of uncertainty representing a state of knowledge can be updated when a new information, which may be pervaded with uncertainty, becomes available. This problem is considered in various framework, namely: Shafer's evidence theory, Zadeh's possibility theory, Spohn's theory of epistemic states. In the two first cases, analogues of Jeffrey's rule of conditioning are introduced and discussed. The relations between Spohn's model and possibility theory are emphasized and Spohn's updating rule is contrasted with the Jeffrey-like rule of conditioning in possibility theory. Recent results by Shenoy on the combination of ordinal conditional functions are reinterpreted in the language of possibility theory. It is shown that Shenoy's combination rule has a well-known possibilistic counterpart.
Valuation-Based Systems for Discrete Optimization
Venue: arXiv cs.AI 2013
Year: 2013

This paper describes valuation-based systems for representing and solving discrete optimization problems. In valuation-based systems, we represent information in an optimization problem using variables, sample spaces of variables, a set of values, and functions that map sample spaces of sets of variables to the set of values. The functions, called valuations, represent the factors of an objective function. Solving the optimization problem involves using two operations called combination and marginalization. Combination tells us how to combine the factors of the joint objective function. Marginalization is either maximization or minimization. Solving an optimization problem can be simply described as finding the marginal of the joint objective function for the empty set. We state some simple axioms that combination and marginalization need to satisfy to enable us to solve an optimization problem using local computation. For optimization problems, the solution method of valuation-based systems reduces to non-serial dynamic programming. Thus our solution method for VBS can be regarded as an abstract description of dynamic programming. And our axioms can be viewed as conditions that permit the use of dynamic programming.
On Some Equivalence Relations between Incidence Calculus and Dempster-Shafer Theory of Evidence
Venue: arXiv cs.AI 2013
Year: 2013

Incidence Calculus and Dempster-Shafer Theory of Evidence are both theories to describe agents' degrees of belief in propositions, thus being appropriate to represent uncertainty in reasoning systems. This paper presents a straightforward equivalence proof between some special cases of these theories.
Using Belief Functions for Uncertainty Management and Knowledge Acquisition: An Expert Application
Venue: arXiv cs.AI 2013
Year: 2013

This paper describes recent work on an ongoing project in medical diagnosis at the University of Guelph. A domain on which experts are not very good at pinpointing a single disease outcome is explored. On-line medical data is available over a relatively short period of time. Belief Functions (Dempster-Shafer theory) are first extracted from data and then modified with expert opinions. Several methods for doing this are compared and results show that one formulation statistically outperforms the others, including a method suggested by Shafer. Expert opinions and statistically derived information about dependencies among symptoms are also compared. The benefits of using uncertainty management techniques as methods for knowledge acquisition from data are discussed.
Analysis in HUGIN of Data Conflict
Venue: arXiv cs.AI 2013
Year: 2013

After a brief introduction to causal probabilistic networks and the HUGIN approach, the problem of conflicting data is discussed. A measure of conflict is defined, and it is used in the medical diagnostic system MUNIN. Finally, it is discussed how to distinguish between conflicting data and a rare case.
How to Approximate A Set Without Knowing Its Size In Advance
Venue: arXiv cs.DS 2013
Year: 2013

The dynamic approximate membership problem asks to represent a set S of size n, whose elements are provided in an on-line fashion, supporting membership queries without false negatives and with a false positive rate at most epsilon. That is, the membership algorithm must be correct on each x in S, and may err with probability at most epsilon on each x not in S. We study a well-motivated, yet insufficiently explored, variant of this problem where the size n of the set is not known in advance. Existing optimal approximate membership data structures require that the size is known in advance, but in many practical scenarios this is not a realistic assumption. Moreover, even if the eventual size n of the set is known in advance, it is desirable to have the smallest possible space usage also when the current number of inserted elements is smaller than n. Our contribution consists of the following results: - We show a super-linear gap between the space complexity when the size is known in advance and the space complexity when the size is not known in advance. - We show that our space lower bound is tight, and can even be matched by a highly efficient data structure.
On the communication complexity of sparse set disjointness and exists-equal problems
Venue: arXiv cs.CC 2013
Year: 2013

In this paper we study the two player randomized communication complexity of the sparse set disjointness and the exists-equal problems and give matching lower and upper bounds (up to constant factors) for any number of rounds for both of these problems. In the sparse set disjointness problem, each player receives a k-subset of [m] and the goal is to determine whether the sets intersect. For this problem, we give a protocol that communicates a total of O(k\log^{(r)}k) bits over r rounds and errs with very small probability. Here we can take r=\log^{*}k to obtain a O(k) total communication \log^{*}k-round protocol with exponentially small error probability, improving on the O(k)-bits O(\log k)-round constant error probability protocol of Hastad and Wigderson from 1997. In the exist-equal problem, the players receive vectors x,y\in [t]^n and the goal is to determine whether there exists a coordinate i such that x_i=y_i. Namely, the exists-equal problem is the OR of n equality problems. Observe that exists-equal is an instance of sparse set disjointness with k=n, hence the protocol above applies here as well, giving an O(n\log^{(r)}n) upper bound. Our main technical contribution in this paper is a matching lower bound: we show that when t=Ω(n), any r-round randomized protocol for the exists-equal problem with error probability at most 1/3 should have a message of size Ω(n\log^{(r)}n). Our lower bound holds even for super-constant r <= \log^*n, showing that any O(n) bits exists-equal protocol should have \log^*n - O(1) rounds.
Sparse FGLM algorithms
Venue: arXiv cs.SC 2013
Year: 2013

Given a zero-dimensional ideal I in K[x1,...,xn] of degree D, the transformation of the ordering of its Groebner basis from DRL to LEX is a key step in polynomial system solving and turns out to be the bottleneck of the whole solving process. Thus it is of crucial importance to design efficient algorithms to perform the change of ordering. The main contributions of this paper are several efficient methods for the change of ordering which take advantage of the sparsity of multiplication matrices in the classical FGLM algorithm. Combing all these methods, we propose a deterministic top-level algorithm that automatically detects which method to use depending on the input. As a by-product, we have a fast implementation that is able to handle ideals of degree over 40000. Such an implementation outperforms the Magma and Singular ones, as shown by our experiments. First for the shape position case, two methods are designed based on the Wiedemann algorithm: the first is probabilistic and its complexity to complete the change of ordering is O(D(N1+nlog(D))), where N1 is the number of nonzero entries of a multiplication matrix; the other is deterministic and computes the LEX Groebner basis of the radical of I via Chinese Remainder Theorem. Then for the general case, the designed method is characterized by the Berlekamp-Massey-Sakata algorithm from Coding Theory to handle the multi-dimensional linearly recurring relations. Complexity analyses of all proposed methods are also provided. Furthermore, for generic polynomial systems, we present an explicit formula for the estimation of the sparsity of one main multiplication matrix, and prove its construction is free. With the asymptotic analysis of such sparsity, we are able to show for generic systems the complexity above becomes $O(\sqrt{6/n π} D^{2+(n-1)/n}})$.
Fast Approximate L_infty Minimization: Speeding Up Robust Regression
Venue: arXiv cs.CV 2013
Year: 2013

Minimization of the $L_\infty$ norm, which can be viewed as approximately solving the non-convex least median estimation problem, is a powerful method for outlier removal and hence robust regression. However, current techniques for solving the problem at the heart of $L_\infty$ norm minimization are slow, and therefore cannot scale to large problems. A new method for the minimization of the $L_\infty$ norm is presented here, which provides a speedup of multiple orders of magnitude for data with high dimension. This method, termed Fast $L_\infty$ Minimization, allows robust regression to be applied to a class of problems which were previously inaccessible. It is shown how the $L_\infty$ norm minimization problem can be broken up into smaller sub-problems, which can then be solved extremely efficiently. Experimental results demonstrate the radical reduction in computation time, along with robustness against large numbers of outliers in a few model-fitting problems.
What really happened on September 15th 2008? Getting The Most from Your Personal Information with Memacs
Venue: arXiv cs.HC 2013
Year: 2013

Combining and summarizing meta-data from various kinds of data sources is one possible solution to the data fragmentation we are suffering from. Multiple projects have addressed this issue already. This paper presents a new approach named Memacs. It automatically generates a detailed linked diary of our digital artifacts scattered across local files of multiple formats as well as data silos of the internet. Being elegantly simple and open, Memacs uses already existing visualization features of GNU Emacs and Org-mode to provide a promising platform for life-logging, Quantified Self movement, and people looking for advanced Personal Information Management (PIM) in general.